A mathematical curve and surface visualiser for singular surface and objects from Singularity Theory.
The program can calculate many of the objects found in Singularity theory:
Algebraic curves defined by a single polynomial equation in two variables. e.g. a circle
x^2 + y^2 - r^2;
Algebraic surfaces defined by a single polynomial equation in three variables. e.g. a cone
x^2 + y^2 - z^2;
Paramertised curves defined by a 3D vector expression in a single variable. e.g. a helix
[cos(pi t), sin(pi t), t];
Parameterised surfaces defined by a 3D vector expression in two variables. e.g. a cross-cap
Intersection of surfaces with sets defined by an equation. Can be used to calculate non-polynomial curves.
Mapping from R^3 to R^3 defined by 3D vector equation in three variables. e.g. a rotation
[cos(pi th) x - sin(pi th) y,sin(pi th) x + cos(pi th) y,z];
Intersections where the equation depends on the definition of another curve or surface. e.g. The profile of a surface
N . [A,B,C]; N = diff(S,x) ^^ diff(S,y);
Mappings where the equation depends on another surface. For example projection of a curve onto a surface.
Intersections where the equations depends on a pair of curves. For example the pre-symmetry set of a curve.
Mapping where the equation depends on a pair of curves. For example the Symmetry set.
The program requires
- Java any recent version
- JavaView mathematical visualization software from javaview.de Alas not open-source
- JEP 2.4.1 Java Expression Parser, a mathematical parser evaluator from jep-java-gpl or my own fork jep-java-gpl which may contain some customisation of the package to fit the needs of the SingSurf program.
It is a good idea to register your version of JavaView. Regestration provides a licence file
jv-lic.lic which should be copied to the
rsrc directory, this prevents a notification message appearing.
Installation and running
A zip file with an executable jar file and all necessary files is availiable from singsurf.org. Once unpacked this can be run using a single line java command.
For the git source code, there are three different main classes
org.singsurf.singsurf.SingSurfProthe 3D version with all sub-types
org.singsurf.singsurf.SingSurf2Dthe 2D version optimised for curves in the plane
org.singsurf.singsurf.ASurfSimpa simplified version just with the algebraic surface component